We have seen that it is possible that most of the baryons were processed
through
a first generation of pregalactic or protogalactic stars and henceforth
the term
"Population III" is used specifically in this sense. However, it should
be stressed
that the cosmological interest in Population III stars is not confined
to the dark
matter issue. They would also be expected to produce radiation,
explosions, and
nucleosynthesis products, and each of these could have important
cosmological consequences
(Carr et al 1984).
Although there are no observations which
unambiguously demand that most of the baryons were processed through
Population III stars, there are theoretical reasons for anticipating
their formation.
This is because the existence of galaxies and clusters of galaxies
implies that
there must have been density fluctuations in the early Universe and, in many
scenarios, these fluctuations would also give rise to a population of
pregalactic
stars. The precise way in which this occurs depends on the nature of the
fluctuations and the nature of the dominant dark matter, as we now discuss.

In a baryon-dominated universe with isothermal or isocurvature density
fluctuations, the first bound objects usually have a mass corresponding
to the
baryonic Jeans mass at decoupling. This is MJb 106b-1/2M, where
b is the
baryon density parameter, and clouds of this mass would bind at a
redshift ~ 100,
depending on the form of the spectrum of fluctuations at decoupling. Larger
bound objects - like galaxies and clusters of galaxies - would then build up
through a process of hierarchical clustering
(Peebles & Dicke 1968).
Regions smaller than MJb, even though their initial
overdensity might be higher, would
not begin to collapse until they were larger than the Jeans length and
by then they
would generally have been erased either by viscous damping prior to
decoupling
or by nonlinear processes during the oscillatory period after decoupling
(Carr & Rees 1984).
However, more exotic possibilities arise if the fluctuation
spectrum is sufficiently steep for the fluctuations to be highly
nonlinear
on smaller scales because, in this case, very small regions could
collapse well before recombination
(Hogan 1978).
Indeed, this is expected in the primordial isocurvature baryon-dominated
model
(Hogan 1993).

In the Cold Dark Matter scenario, in which the density of the Universe
is dominated by cold particle relics, structure also builds up
hierarchically
(Blumenthal et al 1984).
In this case, one expects bound clumps of the particles
to form down to very small scales
(Hogan & Rees 1988),
but baryons would
only fall into the potential wells, forming bound clouds, on baryon
scales above
MJa
106ba-3/2M, where
a is the
cold particle density
(Carr & Rees 1984,
de Araujo & Opher 1990).
In fact, the formation of the pregalactic
clouds is even easier in this case because the cold particle
fluctuations grow by an extra factor of
10a
between the time when the cold particles dominate the density and
decoupling.

In a baryon-dominated universe with adiabatic density fluctuations, the
first objects to form are pancakes of cluster size
(Zeldovich 1970)
because adiabatic
fluctuations are erased by photon diffusion for M <
1013b-5/4M
(Silk 1968).
Galaxies and smaller scale structures therefore have to form as a result of
fragmentation. This scenario appears to be excluded by CMB anistropy
constraints
but a similar picture applies if one has adiabatic fluctuations in a Hot
Dark
Matter scenario, in which the Universe's mass is dominated by a particle
like the
neutrino. In this case, the fluctuations are erased by neutrino
free-streaming for
M < 1015-2M
(Bond et al 1980),
so the first objects to form are pancakes
of supercluster scale. In both scenarios one expects the pancakes to
initially fragment into clumps of mass 108M; these
clumps must then cluster in order
to form galaxies. Even in this case, therefore, one might expect pregalactic
clouds to form, albeit at a relatively low redshift (z < 10).

All of these scenarios would be modified if the Universe contained
topological relics such as strings or textures
(Cen et al 1991).
Such relics could induce
the formation of smaller scale bound regions than usual. For example,
Silk & Stebbins (1993)
find that in the CDM picture with strings, up to 10-3 of
the mass of the Universe could go into cold dark matter clumps at the
time of
matter-radiation equilibrium. These clumps would then accrete baryonic
halos, forming globular-cluster type objects.

In the explosion scenario
(Ostriker & Cowie 1981,
Ikeuchi 1981),
the first
objects to form are explosive seeds (stars or clusters of stars). These
generate
shocks which sweep up vast shells of gas; when the shells overlap, most
of the gas gets compressed into thin sheets
(Carr & Ikeuchi 1985).
The sheets then
fragment either directly into galaxies or into lower-mass systems, depending
on the cooling mechanism
(Bertschinger 1983,
Wandel 1985).
Although the
explosion scenario was originally invoked to explain large-scale
structure, this
now seems to be incompatible with the upper limit on the
y-parameter permitted
by FIRAS. However, one can still envisage this as a mechanism for
amplifying
the fraction of the gas going into stars - an idea applicable in models
with or without nonbaryonic dark matter
(Scherrer 1992).